A353803 a(n) = Product_{p^e||n} sigma(sigma(p^e)) - sigma(sigma(n)), where n = Product_{p^e||n}, with each p^e the maximal power of prime p that divides n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 42, 21, 0, 0, 0, 0, 0, 0, 0, 141, 0, 0, 72, 36, 56, 0, 0, 0, 48, 54, 0, 168, 0, 0, 0, 45, 0, 0, 0, 0, 78, 21, 0, 0, 141, 0, 108, 54, 0, 192, 0, 0, 0, 0, 64, 381, 0, 0, 168, 317, 0, 0, 0, 0, 0, 0, 168, 192, 0, 0, 0, 72, 0, 336, 188, 0, 144, 126, 0, 126, 112

Offset

1,10

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to sigma(n)

Formula

a(n) = A353802(n) - A051027(n).

Prog

(PARI)
A051027(n) = sigma(sigma(n));
A353803(n) = { my(f = factor(n)); (prod(k=1, #f~, A051027(f[k, 1]^f[k, 2])) - A051027(n)); };

Crossrefs

Cf. A000203, A051027, A353802, A353804, A353805, A353806.

Cf. A336547 (positions of 0's), A336548 (positions of terms > 0).

Cf. also A353753.

Sequence in context: A340982 A334624 A036483 * A275153 A019313 A276999

Adjacent sequences: A353800 A353801 A353802 * A353804 A353805 A353806

Keyword

nonn

Author

Antti Karttunen, May 08 2022

Status

approved